Method of determining model-specific factors for pattern recognition, in particular for speech patterns

ABSTRACT

A method for recognizing a pattern that comprises a set of physical stimuli, said method comprising the steps of: 
     providing a set of training observations and through applying a plurality of association models ascertaining various measuring values p j (k|x), j=1 . . . M, that each pertain to assigning a particular training observation to one or more associated pattern classes; 
     setting up a log/linear association distribution by combining all association models of the plurality according to respective weight factors, and joining thereto a normalization quantity to produce a compound association distribution; 
     optimizing said weight factors for thereby minimizing a detected error rate of the actual assigning to said compound distribution; 
     recognizing target observations representing a target pattern with the help of said compound distribution.

BACKGROUND OF THE INVENTION

The invention relates to a method for recognizing a pattern that comprises a set of physical stimuli, said method comprising the steps of:

providing a set of training observations and through applying a plurality of association models ascertaining various measuring values p_(j)(k|x), j=1 . . . M, that each pertain to assigning a particular training observation to one or more associated pattern classes;

setting up a log/linear association distribution by combining all association models of the plurality according to respective weight factors, and joining thereto a normalization quantity to produce a compound association distribution.

The invention has been conceived for speech recognition, but is likewise applicable to other recognition processes, such as for speech understanding, speech translation, as well as for recognizing handwriting, faces, scene recognition, and other environments. The association models may be probability models that give probability distributions for assigning patterns to classes. Other models can be based on fuzzy logic, or similarity measures, such as distances measured between target and class. Known technology has used different such models in a combined recognition attack, but the influences lent to the various cooperating models were determined in a haphazard manner. This meant that only few and/or only elementary models were feasible.

The present inventor has recognized that the unification of Maximum-Entropy and Discriminative Training principles would in case of combination of more than one model in principle be able to attain superior results as compared with earlier heuristic methods. Also, a straightforward data processing procedure should provide a cheap and fast road to those results.

In consequence, amongst other things, it is an object of the invention to evaluate a log-linear combination of various ‘sub’models p_(j)(k|X) whilst executing parameter evaluation through discriminative training. Now, according to one of its aspects, the invention attains the object by recognizing a pattern that comprises a set of physical stimuli, said method comprising the steps of:

providing a set of training observations and through applying a plurality of association models ascertaining various measuring values p_(j)(k|x), j=1 . . . M, that each pertain to assigning a particular training observation to one or more associated pattern classes;

setting up a log/linear association distribution by combining all association models of the plurality according to respective weight factors, and joining thereto a normalization quantity to produce a compound association distribution;

optimizing said weight factors for thereby minimizing a detected error rate of the actual assigning to said compound distribution;

recognizing target observations representing a target pattern with the help of said compound distribution. Inter alia, such procedure allows to combine any number of models into a single maximum-entropy distribution. Furthermore, it allows an optimized interaction of models that may vary widely in character and representation.

The invention also relates to a method for modelling an association distribution according to the invention. This provides an excellent tool for subsequent users of the compound distribution for recognizing appropriate patterns.

The invention also relates to a method for recognizing patterns using a compound distribution produced by the invention. This method has users benefitting to a great deal by applying the tool realized by the invention.

The invention relates to a system that is arranged for practicing a method according to the invention. Further aspects are recited in dependent Claims.

BRIEF DESCRIPTION OF THE DRAWING

These and other aspects and advantages of the invention will be discussed. more in detail with reference to the detailed disclosure of preferred embodiments hereinafter, and in particular with reference to the appended Figures that show:

FIG. 1, an overall flow chart of the method; and

FIG. 2, a comprehensive system for practicing the invention.

DETAILED DISCLOSURE OF PREFERRED EMBODIMENTS

The invention being based on a balanced application of mathematics on the handling and accommodating of physical quantities that may be of very diverse character, much of the disclosure is based on advanced mathematics. However, both the starting point and the eventual outcome have permanently physical aspects and relevance. The speech recognition may be used to control various types of machinery. Scene analysis may guide unmanned vehicles. Picture recognition may be used for gate control. Various other applications are evident per se. The expressions hereinafter are numbered in sequence, and will be referred to in the text by these numbers.

The invention determines model-specific factors in order to combine and optimize several different models into a single pattern recognition process, notably for speech recognition.

The statistical speech recognition method utilizes Bayes' decision theory in order to form an identification mechanism with a minimum error rate. In conformity with this theory, the decision rule is such, that an observation x must be assigned to the class k (xεk for brevity), when for a given a posteriori or “real” probability distribution π(k|x) it holds that: $\begin{matrix} {{{\forall k^{\prime}} = 1},\ldots \quad,{K;\quad {k^{\prime} \neq k};\quad {{{\log \quad \frac{\pi\left( \left. {k{x}} \right) \right.}{\pi \quad \left. \left( {k^{\prime}{x}} \right. \right)}} \geq 0} = {{> x} \in k}}}} & (1) \end{matrix}$

In literature, the term log(π(k|x)/π(k′|x)) is called the discriminant function. Hereinafter, this term will be noted g(x,k,k′) will be used for brevity. When the decision rule (1) is used for recognizing complete sentences, observed expressions x_(l) ^(T)=(x^(l), . . . ,x^(T)), that have a temporal length T, will be classified as spoken word sequences w_(l) ^(S)=(w^(l), . . . w^(s)) of length S. The a posteriori distribution π(w_(l) ^(S)|x_(l) ^(T)) is however unknown since it describes the complicated natural speech communication process of humans. Consequently, it must be approximated by a distribution p(w_(l) ^(S)|x_(l) ^(T)). Thus far, the acoustic-phonetic and grammatical modelling of speech in the form of parametric probability distributions have attained the best results. The form of the distribution p(w_(l) ^(S)|x_(l) ^(T)) is then predetermined; the unknown parameters of the distribution are estimated on the basis of training data. The distribution p(w_(l) ^(S)|x_(l) ^(T)) so acquired is subsequently inserted into Bayes' decision rule. The expression x_(l) ^(T) is then assigned to the word sequence w_(l) ^(S) for which: $\begin{matrix} {{\forall{w_{1}^{{\prime s}^{\prime}} \neq w_{1}^{s}}};\quad {{\log \quad \frac{p\left( \left. {w_{1}^{s}{x_{1}^{T}}} \right) \right.}{p\quad \left. \left( {w_{1}^{{\prime s}^{\prime}}{x_{1}^{T}}} \right. \right)}} > 0}} & (2) \end{matrix}$

Conversion of the discriminant function $\begin{matrix} \begin{matrix} {{g\left( {s_{1}^{T},w_{1}^{s},w_{1}^{{\prime s}^{\prime}}} \right)} = {\log \quad \frac{p\left( \left. {w_{1}^{s}{x_{1}^{T}}} \right) \right.}{p\quad \left. \left( {w_{1}^{{\prime s}^{\prime}}{x_{1}^{T}}} \right. \right)}}} \\ {{= {\log \quad \frac{p\quad \left( w_{1}^{s} \right)\quad {p\left( \left. {x_{1}^{T}{w_{1}^{s}}} \right) \right.}}{p\quad \left( w_{1}^{{\prime s}^{\prime}} \right)p\quad \left( {x_{1}^{T}{{w_{1}^{{\prime s}^{\prime}}}^{)}}} \right.}}},} \end{matrix} & (3) \end{matrix}$

allows to separate the grammatical model p(w_(l) ^(s)) from the acoustic-phonetic model p(x_(l) ^(T)|w_(l) ^(s)) in a natural way. The grammatical model p(w_(l) ^(s)) then describes the probability of occurrence of the word sequence w_(l) ^(s) per se, and the acoustic-phonetic model p(x_(l) ^(T)|w_(l) ^(s)) evaluates the probability of occurrence of the acoustic signal x_(l) ^(T) during the uttering of the word sequence w_(l) ^(s). Both models can then be estimated separately, so that an optimum use can be made of the relatively limited amount of training data. The decision rule (3) could be less than optimum due to a deviation of the distribution p from the unknown distribution π, even though the estimation of the distribution p was optimum. This fact motivates the use of so-called discriminative methods. Discriminative methods optimize the distribution p directly in respect of the error rate of the decision rule as measured empirically on training data. The simplest example of such discriminative optimization is the use of the so-called language model factor λ. The equation (3) is then modified as follows: $\begin{matrix} {{g\left( {x_{1}^{T},w_{1}^{s},w_{1}^{{\prime s}^{\prime}}} \right)} = {\log \quad \frac{p\quad \left( w_{1}^{s} \right)^{\lambda}p\left( \left. {x_{1}^{T}{w_{1}^{s}}} \right) \right.}{p\quad \left( w_{1}^{{\prime s}^{\prime}} \right)^{\lambda}p\quad \left. \left( {x_{1}^{T}{w_{1}^{{\prime s}^{\prime}}}} \right. \right)}}} & (4) \end{matrix}$

Experiments show that the error rate incurred by the decision rule (4) decreases when choosing, λ>1. The reason for this deviation from theory, wherein λ=1, lies in the incomplete or incorrect modelling of the probability of the compound event (w_(l) ^(s),x_(l) ^(T)). The latter is inevitable, since the knowledge of the process generating the event (w_(l),x_(l) ^(T)) is incomplete.

Many acoustic-phonetic and grammatical language models have been analyzed thus far. The object of these analyses was to find the “best” model for the relevant recognition task out of the set of known or given models. All models determined in this manner are however imperfect representations of the real probability distribution, so that when these models are used for pattern recognition, such as speech recognition, incorrect recognitions occur as incorrect assignment to classes.

It is an object of the invention to provide a modelling, notably for speech, which approximates the real probability distribution more closely and which nevertheless can be carried out while applying only little processing effort, and in particular to allow easy integration of a higher number of known or given models into a single classifier mechanism.

SUMMARY OF THE INVENTION

The novel aspect of the approach is that it does not attempt to integrate known speech properties into a single acoustic-phonetic distribution model and into a single grammatical distribution model which would involve complex and difficult training. The various acoustic-phonetic and grammatical properties are now modeled separately and trained id the form of various distributions p_(j)(w_(l) ^(S)|x_(l) ^(T)), j=l . . . M, followed by integration into a compound distribution $\begin{matrix} {p_{\{\Lambda\}}^{\pi} = \left( {\left. {w_{1}^{s}{x_{1}^{T}}} \right) = {{C(\Lambda)} \cdot {\prod\limits_{j = 1}^{M}\quad {p_{j}{\left( {w_{1}^{s}\left. {x_{1}^{T}} \right){^{\lambda_{j}}\quad {= {\exp \left\{ {{\log \quad {C(\Lambda)}} + {\sum\limits_{j = 1}^{M}\quad {\lambda_{j}\log \quad p_{j}\quad \left( \left. {w_{1}^{s}{x_{1}^{T}}} \right) \right\}}}} \right.}}}} \right.}}}}} \right.} & (5) \end{matrix}$

The effect of the model p_(j) on the distribution p_({Λ}) ^(π) is determined by the associated coefficient λ_(j).

The factor C({circumflex over ( )}) ensures that the normalization condition for probabilities is satisfied. The free coefficients {circumflex over ( )}=(λ₁, . . . λ_(M))^(tr) are adjusted so that the error rate of the resultant discriminant function $\begin{matrix} {{g\left( {x_{1}^{T},w_{1}^{s},w_{1}^{{\prime s}^{\prime}}} \right)} = {\log \quad \frac{\prod\limits_{j = 1}^{M}{p_{j}{{\left. \left( {w_{1}^{s}{x_{1}^{T}}} \right. \right)}^{\lambda_{j}}}}}{\prod\limits_{j = 1}^{M}\quad {p_{j}{{\left. \left( {w_{1}^{{\prime s}^{\prime}}{x_{1}^{T}}} \right. \right)}^{\lambda_{j}}}}}}} & (6) \end{matrix}$

is as low as possible. There are various possibilities for implementing of this basic idea, several of which will be described in detail hereinafter.

First of all, various terms used herein will be defined. Each word sequence w_(l) ^(s) forms a class k; the sequence length S may vary from one class to another. A speech utterance x_(l) ^(T) is considered as an observation x; its length T may then differ from one observation to another.

Training data is denoted by the references (x_(n), k), with n=1, . . . ,N; k=0, . . . ,K. Herein N is the number of acoustic training observations x_(n), and k_(n) is the correct class associated with the observation x_(n). Further, k≠k_(n) are the various incorrect rival classes that compete with respect to k_(n).

The classification of the observation x into the class k in conformity with Bayes' decision rule (1) will be considered. The observation x is an acoustic realization of the class k. In the case of speech recognition, each class k symbolizes a sequence of words. However, the method can be applied more generally.

Because the class k_(n) produced by the training observation x_(n) is known, an ideal empirical distribution {circumflex over (π)}(k|x) can be constructed on the basis of the training data (x_(n), k); n=1 . . . N; k=0 . . . K. This distribution should be such that the decision rule derived therefrom has a minimum error rate when applied to the training data. In the case of classification of complete word sequences k, a classification error through selecting an erroneous word sequence k≠k_(n), may lead to several word errors. The number of word errors between the incorrect class k and the correct class k_(n) is called the Levenshtein distance E(k,k_(n)) The decision rule formed from E(k,k_(n)) has a minimum word error rate when a monotony property is satisfied.

The ideal empirical distribution {circumflex over (π)} is a function of the empirical error value E(k,k_(n)) which is given only for the training data, but is not defined with respect to unknown test data, because the correct class assignment is not given in that case. Therefore, on the basis of this distribution there is sought a distribution $\begin{matrix} {p^{\pi}\left\{ \Lambda \right\} \left( {\left. {k{x}} \right) = \frac{\exp \left\{ {\sum\limits_{j = 1}^{M}\quad {\lambda_{j}\log \quad {p_{j}\left( \left. {k{x}} \right) \right\}}}} \right.}{\sum\limits_{k^{\prime} = 1}^{K}\quad {\exp \left\{ {\sum\limits_{j = 1}^{M}\quad {\lambda_{j}\log \quad {p_{j}\left( \left. {k^{\prime}{x}} \right) \right\}}}} \right.}}} \right.} & (7) \end{matrix}$

which is defined over arbitrary, independent test data and has an as low as possible empirical error rate on the training data. If the M predetermined distribution models p₁(k|x), . . . , p_(M)(k|x), are defined on arbitrary test data, the foregoing also holds for the distribution P_({Λ}) ^(π)(k|x). When the freely selectable coefficients Λ=(λ1, . . . , λ_(M))^(tr) (8) are determined in such a manner that p_({Λ}) ^(π)(k|x) on the training data has a minimum error rate, and if the training data is representative, P_({Λ}) ^(π)(k|x) should yield an optimum decision rule also on independent test data.

The GPD method as well as the least mean square method optimize a criterion which approximates the mean error rate of the classifier. In comparison with the GPD method, the least mean square method offers the advantage that it yields a closed solution for the optimum coefficient {circumflex over ( )}.

The least mean square method will first be considered. Because the discriminant function (1) determines the quality of the classifier, the coefficients Λ should minimize the root mean square deviation ${\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\left( {{\log \quad \frac{p_{\bigwedge}\left. \left( {k{x_{n}}} \right. \right)}{p_{\bigwedge}\left. \left( {k_{n}{x_{n}}} \right. \right)}} - {E\left( {k_{n},k} \right)}} \right)^{2}}}} = {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\left( {{\sum\limits_{\quad j}\quad {\lambda_{j}\log \quad \frac{p_{j}\left. \left( {k{x_{n}}} \right. \right)}{p_{j}\left. \left( {k_{n}{x_{n}}} \right. \right)}}} - {E\left( {k_{n},k} \right)}} \right)^{2}}}}$

of the discriminant functions of the distributions p_({Λ}) ^(π)(k|x) from the empirical error rate E(k,k_(n)). The summing over r then includes all rival classes in the criterion. Minimizing D ({circumflex over ( )}) leads to a closed solution for the optimum coefficient vector Λ=Q⁻¹ (9), further detailed by $Q_{i,j} = {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}{\left\{ {\log \quad \frac{p_{i}\left( \left. {k_{n}{x_{n}}} \right) \right.}{p_{i}\left( \left. {k{x_{n}}} \right) \right.}} \right\} \left\{ {\log \quad \frac{p_{j}\left( \left. {k_{n}{x_{n}}} \right) \right.}{p_{j}\left( \left. {k{x_{n}}} \right) \right.}} \right\} \quad {and}}}}}$ $p_{i} = {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}{{E\left( {k_{n},k} \right)}\left\{ {\log \quad \frac{p_{i}\left( \left. {k_{n}{x_{n}}} \right) \right.}{p_{i}\left( \left. {k{x_{n}}} \right) \right.}} \right\}}}}}$

Herein, Q is the autocorrelation matrix of the discriminant functions of the predetermined distribution models. The vector P expresses the relationship between the discriminant functions of the predetermined models and the discriminant function of the distribution {circumflex over (π)}.

The word error rate E(k, k_(n)) of the hypotheses k is thus linearly taken up in the coefficients λ₁, . . . λ_(M). Conversely, the discrimination capacity of the distribution model p_(i) is linearly included in the coefficients λ₁, . . . λ_(M) for determining the coefficients directly via the discriminant function $\log \quad {\frac{p_{i}\left. \left( {k{x_{n}}} \right. \right)}{p_{i}\left. \left( {k_{n}{x_{n}}} \right. \right)}.}$

Alternatively, these coefficients can be determined by using the GPD method. With this method, the smoothed empirical error rate E({circumflex over ( )}): $\begin{matrix} {{E(\Lambda)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\quad l_{({x_{n},k_{n},\Lambda})}}}} & (10) \\ {l_{({x_{n},k_{n0},\Lambda})} = \left( {1 + {A\left( {\frac{1}{K}{\sum\limits_{r = 1}^{K}\quad {\exp \left\{ {{- \eta}\quad \log \frac{p_{(\Lambda)}^{\pi}\left( k_{n} \middle| x_{n} \right)}{p_{(\Lambda)}^{\pi}\left( k \middle| x_{n} \right)}} \right\}}}} \right)}^{- \frac{B}{\eta}}} \right)^{- 1}} & (11) \end{matrix}$

can be directly minimized for the training data. The left hand expression is then a smoothed measure for the error classification risk of the observation x_(n). The values A>0, B>0, η>0 determine the type of smoothing of the error classification risk and should be suitably predetermined. When E(λ) is minimized in respect of the coefficient λ of the log linear combination, the following iteration equation with the step width M is obtained for the coefficients λ_(j), wherein j=1, . . . ,M

λ_(j) ⁽⁰⁾=1 (11), and furthermore according to ${{y_{nk}(\Lambda)} = \left( \frac{p_{\Lambda}\left( k \middle| x_{n} \right)}{p_{\Lambda}\left( k_{n} \middle| x_{n} \right)} \right)^{E_{({k_{n},k})}}},{and}$ ${\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\quad \left( {{\log \frac{p_{\Lambda}\left( k \middle| x_{n} \right)}{p_{\Lambda}\left( k_{n} \middle| x_{n} \right)}} - {E\left( {k_{n},k} \right)}} \right)^{2}}}} = {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\quad \left( {{\sum\limits_{j}\quad {\lambda_{j}\log \frac{p_{j}\left( k \middle| x_{n} \right)}{p_{j}\left( k_{n} \middle| x_{n} \right)}}} - {E\left( {k_{n},k} \right)}} \right)^{2}}}}$

Λ⁽¹⁾=(λ_(l) ⁽¹⁾, . . . , λ_(M) ⁽¹⁾)^(tr); j=1, . . . , M

It is to be noted that the coefficient vector {circumflex over ( )} is included in the criterion E(Λ) by way of the discriminant function $\begin{matrix} {\log \frac{p_{(\Lambda)}^{\pi}\left( k_{n} \middle| x_{n} \right)}{p_{(\Lambda)}^{\pi}\left( k \middle| x_{n} \right)}} & (12) \end{matrix}$

If E({circumflex over ( )}) decreases, the discriminant function (12) should increase on average because of (9) and (10). This results in a further improved decision rule, see (1).

In the above, the aim has been to integrate all available knowledge sources into a single pattern recognition system. Two principles are united. The first is the maximum-entropy principle. This works by introducing as few assumptions as possible, so that uncertainty is maximized. Thus, exponential distributions must be used. In this manner the structure of the sources combination is defined. The second principle is discriminative training, to determine the weighting factors assigned to the various knowledge sources, and the associated models. Through optimizing the parameters, the errors are minimized. For speech, models may be semantic, syntactic, acoustic, and others.

The approach is the log-linear combining of various submodels and the estimating of parameters through discriminative training. In this manner, the adding of a submodel may improve the recognition score. If not, the model in question may be discarded. A submodel can however never decrease the recognition accuracy. In this manner, all available submodels may be combined to yield optimum results. Another application of the invention is to adapt an existing model combination to a new recognition environment.

The theoretical approach of the procedure includes various aspects:

parabolic smoothing of the empirical error rate

simplifying the theory of “minimum error rate training”

providing a closed form solution that needs no iteration sequence.

The invention furthermore provides extra facilities:

estimating an optimum language model factor

applying a log-linear Hidden Markov Model

closed form equations for optimum model combination

closed form equations for discriminative training of class-specific probability distributions.

Now for the classification task specified in (1), the true or posterior distribution π(k|x) is unknown but approximated by a model distribution (p(k|x). The two distribution differ, because of incorrect modelling assumptions and because of insufficient data. An example is the language model factor λ used in. $\left. {\log \frac{{\pi \left( x \middle| k \right)} \cdot {\pi (k)}}{{\pi \left( x \middle| k^{\prime} \right)} \cdot {\pi \left( k^{\prime} \right)}}}\rightarrow{\log \frac{{p\left( x \middle| k \right)} \cdot \left( {p(k)} \right)^{\lambda}}{{p\left( x \middle| k^{\prime} \right)} \cdot \left( {p\left( k^{\prime} \right)} \right)^{\lambda}}} \right.$

The formal definition combines various submodels p_(j)(k|x), j=1 . . . M into a log-linear posterior distribution p_({{circumflex over ( )}})(k|x)=exp {. . . } as given in (5). Next to the log-linear combination of the various submodes, the term log C({circumflex over ( )}) allows normalization to attain a formal probability distribution. The resulting discriminant function is $\begin{matrix} {{\log \frac{p_{(\Lambda)}\left( k \middle| x \right)}{p_{(\Lambda)}\left( k^{\prime} \middle| x \right)}} = {\sum\limits_{j}{\lambda_{j}\log \frac{p_{j}\left( k \middle| x \right)}{p_{j}\left( k^{\prime} \middle| x \right)}}}} & (13) \end{matrix}$

The error rate is minimized and Λ optimized. Optimizing on the sentence level is as follows:

Class k: word sequence

Observation x: spoken utterance (e.g. sentence)

N training samples x_(n), giving the correct sentence

For each sample x_(n)

k_(n): correct class as spoken

k≠k_(n): rival classes, which may be all possible sentences, or for example, a reasonable subset thereof.

Similarity of classes: E(k_(n),k)

E: suitable function of Levenshthein-Distance, or a similarly suitable measure that is monotonous.

Number of words in wordsequence k_(n): L_(n).

Now, equation ${\frac{1}{\sum\limits_{n = 1}^{N}\quad L_{n}}{\sum\limits_{n = 1}^{N}\quad {E\left( {{\arg \quad {\max\limits_{k}\left( {\log \frac{p_{\Lambda}\left( k \middle| x_{n} \right)}{p_{\Lambda}\left( k_{n} \middle| x_{n} \right)}} \right)}},k_{n}} \right)}}} = {\frac{1}{\sum\limits_{n = 1}^{N}\quad L_{n}}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\quad {{E\left( {k_{n},k} \right)} \cdot {\delta \left( {k,{\arg \quad {\max\limits_{k^{\prime}}\left( {\log \frac{p_{\Lambda}\left( k^{\prime} \middle| x_{n} \right)}{p_{\Lambda}\left( k_{n} \middle| x_{n} \right)}} \right)}}} \right)}}}}}$

gives an objective function, the empirical error rate. Herein, the left hand side of the equation introduces the most probable class that bases on the number of erroneous deviations between classes k and k_(n).

The parameters {circumflex over ( )} may be estimated by:

a minimum error rate training through Generalized Probabilistic Descent, which yields an iterative solution.

a modification thereof combines with parabolic smoothing, which yields a closed form solution.

a third method bases on least squares, which again yields a closed form solution.

For the GPD method, the smoothed empirical error rate minimizing is based on. ${L(\Lambda)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\quad {l\left( {x_{n},\Lambda} \right)}}}$

The smoothed misclassification risk is given by, ${l\left( {x_{n},\Lambda} \right)} = \frac{1}{1 + \left( {{AR}_{n}(\Lambda)} \right)^{- B}}$

and the average rivalry by. ${R_{n}(\Lambda)} = \left( {\frac{1}{K - 1}{\sum\limits_{k \neq k_{n}}\quad \left( ^{{E{({k_{n},k})}} \cdot {\sum\limits_{j = 1}^{M}\quad {\lambda_{j}\log \frac{p_{j}{({k|x_{n}})}}{p_{j}{({k_{n}|x_{n}})}}}}} \right)^{\eta}}} \right)^{\frac{1}{\eta}}$

The smoothed empirical error ate is minimized through. ${L(\Lambda)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N_{j}}\quad {l\left( {x_{n},\Lambda} \right)}}}$

Herein, l is a loss function that for straightforward calculations must be differentiatable. Rivalry is given by ${{y_{nk}(\bigwedge)} = \left( \frac{\left. {{{p_{\bigwedge}\left( k \right.}}x_{n}} \right)}{\left. {{{p_{\bigwedge}\left( k_{n} \right.}}x_{n}} \right)} \right)^{E{({k_{n},k})}}},$

wherein E indicates the number of errors. Average rivalry is given through the summing in. ${R_{n}(\bigwedge)} = \left( {\frac{1}{K - 1}{\sum\limits_{\quad {k \neq k_{n}}}\left\lbrack {y_{nk}(\bigwedge)} \right\rbrack^{\eta}}} \right)^{\frac{1}{\eta}}$

A smoothed misclassification risk is used by ${l\left( {x_{n},\Lambda} \right)} = \frac{1}{1 + {{AR}_{n}(\Lambda)}^{- B}}$

that behaves like a sigmoid function. For R_(n)=∞,l becomes zero, for R_(n)=+∞, the limiting value is l=1. Herein A, B are scaling constants greater than zero. Differentiating to {circumflex over ( )} yields, $\begin{matrix} {\lambda_{j}^{({I + 1})} = \quad {\lambda_{j}^{(I)} - {ɛ{\sum\limits_{n = 1}^{N}\quad {{l\left( {x_{n},\bigwedge^{(I)}} \right)}\left( {1 - {l\left( {x_{n},\bigwedge^{(I)}} \right)}} \right) \times}}}}} \\ {\quad \frac{\sum\limits_{k \neq k_{n}}{{E\left( {k_{n},k} \right)}\log \quad {\left( \frac{\left. {{{p_{j}\left( k \right.}}x_{n}} \right)}{\left. {{{p_{j}\left( k_{n} \right.}}x_{n}} \right)} \right)\left\lbrack {y_{nk}\left( \bigwedge^{(I)} \right)} \right\rbrack}^{\eta}}}{\sum\limits_{\quad {k \neq k_{n}}}\left\lbrack {y_{nk}\left( \bigwedge^{(I)} \right)} \right\rbrack^{\eta}}} \end{matrix}$

wherein the vector {circumflex over ( )}^((I)) is given by ⋀^((I)) = (λ₁^((I)), ⋯  , λ_(M)^((I)))^(tr)

and the enventual outcome by. ${y_{nk}(\bigwedge)} = \left( \frac{\left. {{{p_{\bigwedge}\left( k \right.}}x_{n}} \right)}{\left. {{{p_{\bigwedge}\left( k_{n} \right.}}x_{n}} \right)} \right)^{E{({k_{n},k})}}$

The invention also provides a closed form solution for finding the discrimination model combination DMC. The solution is to minimize the distance between on the one hand the discriminant function and on the other hand the ideal discriminant function E(k_(n),k) in a least squares method. The basic expression is given by. ${\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\quad \left( {{\log \frac{p_{\Lambda}\left( k \middle| x_{n} \right)}{p_{\Lambda}\left( k_{n} \middle| x_{n} \right)}} - {E\left( {k_{n},k} \right)}} \right)^{2}}}} = {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\quad \left( {{\sum\limits_{j}\quad {\lambda_{j}\log \frac{p_{j}\left( k \middle| x_{n} \right)}{p_{j}\left( k_{n} \middle| x_{n} \right)}}} - {E\left( {k_{n},k} \right)}} \right)^{2}}}}$

Herein, {circumflex over ( )}=Q⁻¹P, wherein Q is a matrix with elements Q_(ij) given by. $Q_{i,j} = {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{\quad {k \neq k_{n}}}{\left\{ {\log \frac{\left. {{{p_{i}\left( k_{n} \right.}}x_{n}} \right)}{\left. {{{p_{i}\left( k \right.}}x_{n}} \right)}} \right\} \left\{ {\log \frac{\left. {{{p_{j}\left( k_{n} \right.}}x_{n}} \right)}{\left. {{{p_{j}\left( k \right.}}x_{n}} \right)}} \right\}}}}}$

Furthermore, P is a vector with elements P_(i) given by. $P_{i} = {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{\quad {k \neq k_{n}}}{E\left( {k_{n},k} \right)\left\{ {\log \frac{\left. {{{p_{i}\left( k_{n} \right.}}x_{n}} \right)}{\left. {{{p_{i}\left( k \right.}}x_{n}} \right)}} \right\}}}}}$

Now, the empirical error rate has been given earlier in ${\frac{1}{\sum\limits_{n = 1}^{N}\quad L_{n}}{\sum\limits_{n = 1}^{N}{\quad E\quad \left( {{\underset{k}{{argmax}\quad}\left( \frac{\left. {{{\log p_{\bigwedge}\left( k \right.}}x_{n}} \right)}{\left. {{{p_{\bigwedge}\left( k_{n} \right.}}x_{n}} \right)} \right)},k_{n}} \right)}}} = {{\frac{1}{\sum\limits_{n = 1}^{N}\quad L_{n}}{\sum\limits_{n = 1}^{N}{\quad {\sum\limits_{\quad {k \neq k_{n}}}{{{E\left( {k_{n},k} \right)} \cdot \delta}\quad \left( {k,\quad {\underset{k^{\prime}}{{argmax}\quad}\quad \left( {\log \quad \frac{\left. {{{p_{\bigwedge}\left( k^{\prime} \right.}}x_{n}} \right)}{\left. {{{p_{\bigwedge}\left( k_{n} \right.}}x_{n}} \right)}} \right)}} \right)}}}}}}$

For calculatory reasons this is approximated by a smoothed empirical error rate as expressed by. $\frac{1}{\sum\limits_{n = 1}^{N}\quad L_{n}}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{\quad {k \neq k_{n}}}{E{\left( {k,k_{n}} \right) \cdot S}\quad \left( {\log \frac{\left. {{{p_{\bigwedge}\left( k \right.}}x_{n}} \right)}{\left. {{{p_{\bigwedge}\left( k_{n} \right.}}x_{n}} \right)}} \right)}}}$

Herein, an indication is given on the number of errors between k and k_(n) through using a sigmoid function S or a similarly useful function. A useful form is S(x)={(x+B)/(A+B)}², wherein −B<x<A and −B<0<A. for higher values of x, S=1, and for lower values S=0. This parabola has proved to be useful. Various other second degree curves have been found useful. The relevant rivals must now lie in. the central and parabolically curved interval of S. Now, finally, a normalization constraint is added for {circumflex over ( )} according to. ${\sum\limits_{j = 1}^{M}\quad \lambda_{j}} = 1$

The second criterion is solved according to a matrix equation (α, λ^(tr))=Q′⁻¹P′, wherein an additional row and column have been supplemented to matrix Q′ for normalization reasons, according to Q′_(0,0=)0; Q′_(0,j)=1, Q′_(i,0)=½(A+B)². The general element of correlation matrix Q′ has been given in. $\begin{matrix} {Q_{i,j}^{\prime} = \quad {\frac{1}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\quad {E\left( {k,k_{n}} \right)}}}}} \\ {\quad {\left\{ {\log \frac{p_{i}\left( {k_{n}x_{n}} \right)}{\left. {{{p_{i}\left( k \right.}}x_{n}} \right)}} \right\} \left\{ {\log \frac{p_{j}\left( {k_{n}x_{n}} \right)}{\left. {{{p_{j}\left( k \right.}}x_{n}} \right)}} \right\}}} \end{matrix}$

Note that the closed solution is rendered possible through the smoothed step function s. Furthermore, vector P′ likewise gets a normalizing element P₀=1, whereas its general element is given by. P₀^(′) = 1 $P_{i}^{\prime} = {\frac{B}{\left( {K - 1} \right)N}{\sum\limits_{n = 1}^{N}\quad {\sum\limits_{k \neq k_{n}}\quad {E\left( {k,k_{n}} \right)\left\{ {\log \frac{\left. {{{p_{i}\left( k_{n} \right.}}x_{n}} \right)}{\left. {{{p_{i}\left( k \right.}}x_{n}} \right)}} \right\}}}}}$

Experiments have been done with various M-gram language models, such as bigram, trigram, fourgram or tetragram models, various acoustic models, such as word-internal-triphone, cross-word-trigram and pentaphone models. Generally, the automatic DMC procedure performs equally well as the results produced by non-automatic fine tuning using the same set of submodels. However, the addition of extra submodels according to the automatic procedure of the invention allowed to decrease the number of errors by about 8%. This is considered a significant step forward in the refined art of speech recognition. It is expected that the invention could provide similarly excellent results for recognizing other types of patterns, such as signatures, handwriting scene analysis, and the like, given the availability of appropriate sub-models. Other submodels used for broadcast recognition included mllr adaptation, unigram, distance-1 bigram, wherein an intermediate element is considered as don't care, pentaphones and wsj-models. In this environment, raising the number of submodels in the automatic procedure of the invention also lowered the numbers of errors by a significant amount of 8-13%.

FIG. 1 shows an overall flow chart of a method according to the invention. In block 20 the training is started on a set of training data or patterns that is provided in block 22. The start as far as necessary claims required software and hardware facilities; in particular, the various submodels and the identity of the various patterns is also provided. For simplicity, the number of submodels has been limited to 2, but the number may be higher. In parallel blocks 24 and 26, the scores are determined for the individual submodels. In block 28 the log-lin combination of the various submodels is executed and normalized. In block 30 the machine optimizing of vector {circumflex over ( )} in view of the lowest attainable error rate is executed. Note that vector A may have one or more zero-valued components to signal that the associated submodel or -models would bring about no improvement at all.

Next, the vector {circumflex over ( )} and the various applicable submodels will be used for recognizing target data, as shown in the right half of the Figure. The training at left, and the usage at right may be executed remote from each other both in time and in space; for example a person could have a machine trained to that person's voice at a provider's premises. This might require extra data processing facilities. Later, the machine so trained may be used in a household or automobile environment, or other. Thus, blocks 40-46 have corresponding blocks at left.

In block 48 the scorings from the various submodels are log-in combined, using the various components of vector ÷ that had been found in the training. Finally, in block 50 the target data are classified using the results from block 50. In block 52, the procedure is stopped when ready.

FIG. 2 shows a comprehensive system for practicing the invention. The necessary facilities may be mapped on standard hardware, or on a special purpose machine. Item 60 is an appropriate pickup, such as a voice recorder, a two-dimensional optical scanner, together with A/D facilities and quality enhancing preprocessing if necessary. Block 64 represents the processing that applies programs from program memory 66 on data that may arrive from pickup 60, or from data storage 62, where they may have been stored permanently or transiently, after forwarding from pickup 60. Line 70 may receive user control signals, such as start/stop, and possibly training-supportive signals, such as for definitively disabling a non-contributory submodel.

Block 68 renders the recognition result usable, such as by tabulating, printing, addressing a dialog structure for retrieving a suitable speech answer, or selecting a suitable. output control signal. Block 72 symbolizes the use of the recognized speech, such as outputting a speech riposte, opening a gate for a recognized person, selecting a path in a sorting machine, and the like. 

What is claimed is:
 1. A method for modelling an association distribution for a plurality of patterns, said method comprising: receiving a plurality of association models indicating various measuring values p_(j)(k|x), j=1 . . . M; combining said plurality of association models in accordance with a set of weight factors to produce a log/linear association distribution; joining a normalization quantity to said log/linear association distribution to produce a compound association distribution; and optimizing said set of weight factors to minimize a detected error rate of an actual assigning to said compound association distribution, said optimizing of said set of weight factors being effected in a least squares method between an actual discriminant function and an ideal discriminant function, said actual discriminant function resulting from said compound association distribution, and said ideal discriminant function expressed on a basis of an error rate as smoothed through representing said error rate as a second degree curve in an interval (−B,A); and expressing a first weight factor Λ of said set of weight factors in a closed expression Λ=Q⁻¹ P, wherein said first weight factor Λ is normalized through a constraining Σ λ_(j)=1, said Q is an autocorrelation matrix of a set of discriminant functions of said plurality of association models as extended by an addition of a first normalization item, and said P is an correlation vector between said error rate, said actual discriminant function and said ideal discriminant function as extended by an addition of a second normalization item.
 2. The method of claim 1, further comprising: receiving a set of training observations, wherein each association model of said plurality of association models pertains to assigning a particular training observation of said set of training observations to at least one associated pattern class.
 3. The method of claim 1, wherein each association model of said plurality of association models is a first probability model, and said compound association distribution is a second probability model for associating.
 4. The method of claim 3, wherein said first probability model is at least one model from a set of models including a language model, an acoustic model, a mllr adaption model, a unigram model, a distance-1 bigram model, a pentaphone model, and a wsj-model, and said second probability model is at least one model from a set of models.
 5. The method of claim 1, further comprising: recognizing a set of target observations representing a target pattern with a help of said compound association distribution.
 6. A system for modelling an association distribution for a plurality of patterns, said system comprising: a storage means for storing a plurality of association models indicating various measuring values p_(j)(k|x), j=1 . . . M; a first processing means for combining said plurality of association models in accordance with a set of weight factors to produce a log/linear association distribution; a second processing means for joining a normalization quantity to said log/linear association distribution to produce a compound association distribution; a third processing means for optimizing said set of weight factors to minimize a detected error rate of an actual assigning to said compound association distribution, said optimizing of said set of weight factors being effected in a least squares system between an actual discriminant function and an ideal discriminant function, said actual discriminant function resulting from said compound association distribution, and said ideal discriminant function expressed on a basis of an error rate as smoothed through representing said error rate as a second degree curve in an interval (−B,A); and a fourth processing means for expressing a first weight factor Λ of said set of weight factors in a closed expression Λ=Q⁻¹P, wherein said first weight factor Λ is normalized through a constraining Σ λ_(j)=1, said Q is an autocorrelation matrix of a set of discriminant functions of said plurality of association models as extended by an addition of a first normalization item, and said P is an correlation vector between said error rate, said actual discriminant function and said ideal discriminant function as extended by an addition of a second normalization item.
 7. The system of claim 6, further comprising: a pickup means for receiving a set of training observations, where each association model of said plurality of association models pertains to assigning a particular training observation of said set of training observations to at least one associated pattern class.
 8. The system of claim 6, wherein each association model of said plurality of association models is a first probability model, and said compound association distribution is a second probability model for associating.
 9. The system of claim 8, wherein said first probability model is at least one model from a set of models including a language model, an acoustic model, a mllr adaption model, a unigram model, a distance-1 bigram model, a pentaphone model, and a wsj-model, and said second probability model is at least one model from a set of models.
 10. The system of claim 6, further comprising: a recognizing means for recognizing a set of target observations representing a target pattern with a help of said compound association distribution. 